Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


Türk cent


    Turkish classical music uses Pythagorean tuning. A very good approximation to this is provided by 53edo, one degree of which is nearly the same as both the Pythagorean comma and the syntonic comma. Turkish theorists have further subdivided the 53edo degree into 20 parts, making 1060 to the "8ve".

    The Türk cent is thus calculated as the 1060th root of 2, or 2(1/1060), with a ratio of approximately 1:1.000654126. It is an irrational number. The width of the Türk cent is ~1.132075472 (~1 1/8) cents, ~28.3990566 (~28 2/5) jots, ~34.74398887 (~34 3/4) tuning-units, ~46.36981132 (~46 1/3) cawapus, and ~185.4792453 (~185 1/2) midipus.

    There are exactly 88 1/3 Türk cents in a Semitone.

    The formula for calculating the Türk-cents-value of any ratio is:

    Türk-cents = log10(ratio) * [ 1060 / log10(2) ]


    Türk-cent-sizes for some small intervals, with regular (Ellis) cents-values given for comparison:

          interval           Türk-cents            (Ellis) cents
    
    Pythagorean comma   ~20.72300917 (~20 5/7)      ~23.46001038
         53edo degree    20                         ~22.64150943
       syntonic comma   ~18.99722248 (~18 359/360)   ~21.5062896
              kleisma    ~7.161429661 (~7 1/6)       ~8.107278862
          heptameride    ~3.521594684 (~3 1/2)       ~3.986710963
               savart    ~3.533333333 (3 8/15)        4
                 grad    ~1.726917431 (~1 5/7)       ~1.955000865
              skhisma    ~1.725786696 (~1 5/7)       ~1.953720788
             milli8ve     1.06 (1 3/50)               1.2
                 cent    ~0.883333333 (53/60 = ~8/9)  1
             monzisma    ~0.258282877 (~1/4)         ~0.29239571
                  jot    ~0.035212437 (~1/28)        ~0.039863137
          tuning-unit    ~0.028781957 (~1/35)        ~0.032583348
               cawapu    ~0.021565755 (~1/46)        ~0.024414062
               midipu    ~0.005391439 (~1/185)       ~0.006103516
    

    See also Manuel Op de Coul's Logarithmic Interval Measures.

    [from Joe Monzo, JustMusic: A New Harmony]


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